Cost curves for energy: Difference between revisions

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This page is a knowledge crystal of subtype variable. The page identifier is Op_en5478
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Question

What costs curves should be used for different energy products?

Answer

Cost curves for energy: Difference between revisions(-)
Obs	Row	Actor	Fuel	Use	Reference	Unit	Parameters	Description
1	1	Kuopion energia	Coal and peat	Demand	Current	€,ton	0, -0.06
2	2	Kuopio market	Coal and peat	Supply	Current	€,ton	0, 0.5

Parameter c_i are estimated from data: it is the current supply or demand given the current price (used as the point where p = 0).

Rationale

For detailed rationale, see Energy balance.

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Sigma f_i(p) = \Sigma (a_i p^2 + b_i p + c_i) = 0}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p = \frac{-\Sigma b_i \pm \sqrt{(\Sigma b_i)^2 - 4 \Sigma a_i \Sigma c_i}} {2 \Sigma a_i}}

Cost curves are parameterised in the way that the current price p = 0 and therefore the current supply or demand is c_i.

When a demand or supply changes, a new price p must be calculated based on f_i, and then the supplies and demands of other actors can be calculated, resulting in a new balance.

----#: . There is an alternative way to describe the functions:

Zero price is considered as 0 €/product unit. The true market price must be known. This function's parameters are more difficult to estimate. --Jouni 06:16, 28 January 2012 (EET) (type: truth; paradigms: science: comment)

----#: . There is also alternative possibilities for functional forms (p is the price of the product):

Exponential: P0 + P1 * exp(P2*p - P3) --Jouni 17:04, 28 January 2012 (EET) (type: truth; paradigms: science: comment)

Dependencies

Formula

+ Show code - Hide code


formula.Op_en5478 <- function(x) {
	data <- tidy(op_baseGetData("opasnet_base", x$curves[1]), direction = "wide")
	curves <- strsplit(as.character(data$Parameters), split = ",")
	coefficients <- data.frame(array(NA, dim = c(length(curves), 10)))

	for(j in 1:length(curves)) {
		coefficients[j, 1:length(curves[[j]])] <- curves[[j]]
	}
	for(k in 1:ncol(coefficients)) {
		coefficients[, k] <- ifelse(is.na(coefficients[, k]), 0, as.numeric(coefficients[, k]))
	}
	x.new <- polyroot(as.vector(colSums(coefficients)))
	x.new <- min(abs(ifelse(abs(Im(x.new)) < 1e-6, Re(x.new), 1e+30)))
	ys.new <- 0
	for(k in 1:ncol(coefficients)) {
		ys.new <- ys.new + coefficients[, k] * x.new^(k-1)
	}
print(data)
	print(coefficients)
	print(x.new)
print(ys.new)

	return(ys.new)
}


dependencies.Op_en5478 <- list(
	curves = c("Op_en5478", "Cost curves for energy")
)

out <- formula.Op_en5478(dependencies.Op_en5478)
print(out)

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